Anne-Marie Duff. 'She's strong but vulnerable, with a beautiful and very expressive face,' Eyre says. Photograph: Nadav Kander; originally published in the New York Times Magazine. Click on image for full portrait.

Why are there so many great British theatre actors? I have a few theories. First, Shakespeare is the DNA of our theatre and we have a living relationship to his work – it's not just part of heritage Britain. Thanks to Shakespeare, British actors tend to have a sense of history as well as great verbal dexterity and literacy.

And then so many of the characteristics of theatre coincide with the features of our nation: dressing up, processions, ceremonies and social rituals. Adversarial conflict is the stuff of our parliamentary and legal system, and theatre depends on it. British actors, like British politicians, are entirely pragmatic, with a genius for adapting to all conditions and resources. And theatre is concerned with role-playing, which is second nature to a nation obsessed with class distinction and inured to the necessity of pretending to be what you aren't.

Third, our publicly funded not-for-profit theatre has nurtured our great actors. There was an eruption of creative talents in the 60s – writers, actors, directors and designers – which has continued, supported by public subsidy. The index of the success of our theatre has been quality rather than profit, and the National Theatre, Royal Shakespeare Company, Royal Court, regional and fringe theatres have enriched the commercial theatre – in all senses.

But. We produce great actors because we're repressed as a nation. We're introverted and need to be licensed to express ourselves publicly. People say that all changed with Diana, but I think her death just proves my point: it gave us licence to show emotion in public.

All actors crave approval, but however fine an actor's characterisation, you don't make the distinction between approving the performance and approving the actor. In applauding a performance, you bestow love not on the fictional character, but on the actor. "Scratch an actor," Laurence Olivier said, "and you find an actor."

He should have known, but I don't think it's true, or any more true of actors than it is of politicians, priests, teachers, strippers or anyone else engaged in acts of public self-display. What is true, I think, is that if you scratch an actor, you'll find a child. Not that actors are inherently less mature than politicians, priests, etc, but an actor must retain a child's appetite for mimicry, for demanding attention and, above all, for playing.

There are some directors who simply don't like actors. They tend not to work in the theatre. In film, it's different. It's possible to direct a film and hardly speak to the actors. I find that incomprehensible. I admire good actors not only because they do something I'm not capable of, but because the best do it apparently effortlessly.

There is a common myth that actors are all extroverts, but many of the best are rather shy and not especially articulate. I've worked with many of the actors photographed here and they're all undemonstrative people. Judi Dench is the paradigm. She's a bright, warm, witty, reserved woman who doesn't show off publicly or privately. She has an intense empathy with everyone she meets. One of the things that makes a good actor is the ability to imagine what other people are feeling. It's a rare quality – the ability to forget yourself and identify with another person. It's hard to avoid making Judi sound like Maria von Trapp – full of sober virtues – but to suggest this would be to conceal the side of her personality that's in some ways the essence of her: her love of betting, of raucous company, her impish sense of humour.

I've just finished shooting Henry IV with Simon Russell Beale as Falstaff. He's probably the cleverest actor I've worked with. What's rare is to be able to shed that cleverness when you act. You never feel that his internal commentator is visible. The last thing you want is someone showing off their intelligence, commenting on a performance as they're performing it. Simon's a brilliant musician, and as an actor he has perfect pitch – his timing, rhythm and physical coordination have a musical fluency. He's a phenomenon.

A few years ago, I worked with Vinette Robinson when she played Antigone. She's strikingly attractive, articulate and lively without being flamboyant. I've never met Bertie Carvel, but I've seen him in Matilda. His Miss Trunchbull is a marvellous creation. He makes it possible to look at a man playing a woman and believe in his femininity, however grotesque. It's wonderful how a theatre audience can willingly join the conspiracy. Theatre, like religion, can make us believe in the unbelievable.

I worked with Daniel Kaluuya on a short film, I think soon after he left school. He absolutely fits my repression theory, because he's shy and modest but funny and eloquent. He writes well, too.

One of Anne-Marie Duff's first jobs was a small part in an Eduardo de Filippo play I directed at the NT. She later played Cordelia when I directed King Lear. I've always been impressed by how precise and conscientious she is, and how open and guileless. She's strong but vulnerable, with a beautiful and very expressive face. Often, beautiful people on stage seem plain because their beauty isn't animated by talent. In Judi and Anne-Marie, you see the opposite: neither is conventionally beautiful, but on stage they're ravishing.

At his best, Mark Rylance is in a constellation of his own – as he was in Jerusalem. He's singular and unclubby, an exceptional, idiosyncratic actor who feels more like a creature of the late 60s, from a culture that seems at odds with the 21st century.

Eileen Atkins is a Zen actress, everything distilled to its essence: never a wasted gesture. She is fiercely intelligent, and at times intelligently fierce, but a good and forgiving friend.

Patrick Stewart is where my theory of repression falls apart. He doesn't hold back in public or private. He's a wonderful advertisement for the export of character actors from the British subsidised theatre. He was the backbone of the RSC for years before he got into orbit with Star Trek.

The best actors are usually the best company. If you told me, "You're going to have an evening out with everyone in these pictures", I'd think, thanks, I'm going to have a matchlessly good night.